Advances in Difference Equations
Volume 2010 (2010), Article ID 985982, 15 pages
Research Article

Determining Consecutive Periods of the Lorenz Maps

School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310012, China

Received 18 October 2009; Revised 27 February 2010; Accepted 19 May 2010

Academic Editor: Roderick Melnik

Copyright © 2010 Fulai Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Based on symbolic dynamics, the paper provides a satisfactory and necessary condition of existence for consecutive periodic orbits of the Lorenz maps. In addition, a new algorithm with computer assistance based on symbolic dynamics is proposed to find all periodic orbits up to a certain number with little computer time. Examples for consecutive periods of orbits are raised for the Lorenz maps. With a little variation, the theorems and algorithm can be applied to some other dynamic systems.